Refining Euler and fourth-order Runge-Kutta methods using curvature-based adaptivity
This paper introduces curvature-adaptive variants of both the Euler and Runge-Kutta methods for solving ordinary differential equations (ODEs). By incorporating local curvature information into step size selection, the proposed Curvature-Adaptive Euler (CAE) and Curvature-Adaptive fourth-order Rung...
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| Format: | Article |
| Language: | English |
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Institute of Sciences and Technology, University Center Abdelhafid Boussouf, Mila
2025-07-01
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| Series: | Journal of Innovative Applied Mathematics and Computational Sciences |
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| Online Access: | https://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/1922 |
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| _version_ | 1849430704238100480 |
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| author | Anes MOULAI-KHATIR |
| author_facet | Anes MOULAI-KHATIR |
| author_sort | Anes MOULAI-KHATIR |
| collection | DOAJ |
| description |
This paper introduces curvature-adaptive variants of both the Euler and Runge-Kutta methods for solving ordinary differential equations (ODEs). By incorporating local curvature information into step size selection, the proposed Curvature-Adaptive Euler (CAE) and Curvature-Adaptive fourth-order Runge-Kutta (CARK4) methods achieve a superior balance between accuracy and computational efficiency compared to their fixed-step counterparts. The unified curvature adaptation framework presented in this work enhances classical ODE solvers by leveraging the geometric properties of the solution curve, resulting in more efficient numerical integration schemes.
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| format | Article |
| id | doaj-art-efbf87a5fd404637bb673662dc764936 |
| institution | Kabale University |
| issn | 2773-4196 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Institute of Sciences and Technology, University Center Abdelhafid Boussouf, Mila |
| record_format | Article |
| series | Journal of Innovative Applied Mathematics and Computational Sciences |
| spelling | doaj-art-efbf87a5fd404637bb673662dc7649362025-08-20T03:27:52ZengInstitute of Sciences and Technology, University Center Abdelhafid Boussouf, MilaJournal of Innovative Applied Mathematics and Computational Sciences2773-41962025-07-015110.58205/jiamcs.v5i1.1922Refining Euler and fourth-order Runge-Kutta methods using curvature-based adaptivityAnes MOULAI-KHATIR0https://orcid.org/0000-0002-8267-7458University of Oran 2 Mohamed Ben Ahmed This paper introduces curvature-adaptive variants of both the Euler and Runge-Kutta methods for solving ordinary differential equations (ODEs). By incorporating local curvature information into step size selection, the proposed Curvature-Adaptive Euler (CAE) and Curvature-Adaptive fourth-order Runge-Kutta (CARK4) methods achieve a superior balance between accuracy and computational efficiency compared to their fixed-step counterparts. The unified curvature adaptation framework presented in this work enhances classical ODE solvers by leveraging the geometric properties of the solution curve, resulting in more efficient numerical integration schemes. https://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/1922EulerRunge-Kutta 4Curvature |
| spellingShingle | Anes MOULAI-KHATIR Refining Euler and fourth-order Runge-Kutta methods using curvature-based adaptivity Journal of Innovative Applied Mathematics and Computational Sciences Euler Runge-Kutta 4 Curvature |
| title | Refining Euler and fourth-order Runge-Kutta methods using curvature-based adaptivity |
| title_full | Refining Euler and fourth-order Runge-Kutta methods using curvature-based adaptivity |
| title_fullStr | Refining Euler and fourth-order Runge-Kutta methods using curvature-based adaptivity |
| title_full_unstemmed | Refining Euler and fourth-order Runge-Kutta methods using curvature-based adaptivity |
| title_short | Refining Euler and fourth-order Runge-Kutta methods using curvature-based adaptivity |
| title_sort | refining euler and fourth order runge kutta methods using curvature based adaptivity |
| topic | Euler Runge-Kutta 4 Curvature |
| url | https://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/1922 |
| work_keys_str_mv | AT anesmoulaikhatir refiningeulerandfourthorderrungekuttamethodsusingcurvaturebasedadaptivity |